Question

Please attach the solution step by step, thanks!

1. An insurance company collected $31.0 million in premiums and disbursed $28 million in losses. Loss adjustment expenses amounted to $5.0 million. The firm is profitable

A. if dividends paid to policyholders is $4 million and income generated on investments is $4 million.

B. if dividends paid to policyholders is $10 million and income generated on investments is $14 million.

C. if dividends paid to policyholders is $6 million and income generated on investments is $2 million.

D. if dividends paid to policyholders is $10 million and income generated on investments is $4 million.

E. if dividends paid to policyholders is $4 million and income generated on investments is $2 million.

2.

You start an annuity with $1million and expect to receive 12 equal payments beginning at the end of the first year. The guaranteed annual interest rate is 8 percent. The annual payments that you expect to collect are

A. $88,333.33.

B. $119,277.03.

C. $126,368.71.

D. $132,695.02.

E. $144,250.52.

3.

Calculate the annual cash flows of a $2 million, 10-year fixed-payment annuity earning a guaranteed 6 percent annually if the payments are to begin at the end of the year.

A. $137,990.27.

B. $271,735.92.

C. $275,980.53.

D. $280,000.00.

E. $298,058.98.

Answer 1

1. The income in premium =31
The loss =28
Loss Adjustment expense =5
Net loss =31-28-5 =-2
Option B. if dividends paid to policyholders is $10 million and income generated on investments is $14 million.is correct option because
Net Retained profit =14-10 =4 Since this value is greater than loss of -2 hence it creates profit

2. PV =1000000
Rate =8%
Number of Periods =12
Annuity =PV/((1-(1+r)^-n)/r) =1000000/((1-(1+8%)^-12)/8%) =$132,695.02 (Option d is correct option)

3. PV =2000000
Rate =6%
Number of Periods =10
Annuity =PV/((1-(1+r)^-n)/r) =2000000/((1-(1+6%)^-10)/6%) =$271,735.92.(Option b is correct option)